Different qualities aren't limited only to wild pets—many rare World drops and special non-wild companions have had their stats boosted. For example, the world-drop dragon whelps (Azure Whelpling, Crimson Whelpling, Dark Whelpling, and Emerald Whelpling) are of [rare] quality. Check your Pet Journal to see the color-coded rarity of your non-wild pets.
The quality of captured wild pets is random. As of patch 5.1, upon entering a battle the Pet Battle UI shows the quality of a wild pet (idicated by a color-coded border around its icon). If you're farming a specific quality, if you forfeit the match your team will incur a small damage penalty (roughly 10%). There is no accurate way to determine a pet's quality prior to the start of a battle.

Since the same client is used for both our stress test users and our normal beta users, the name in the Battle.net App has changed to “Beta & Stress Test: WoW Classic.” If you’ve been selected to participate in the stress test, you’ll see this option appear in the Region/Account drop down menu so you can download and install the WoW Classic client in advance, but you’ll only be able to see the stress test realm when it becomes available.

World of Warcraft Classic lets you play the game as it existed almost 15 years ago, upon the release of the 1.12 "Drums of War" update. Blizzard says it considers that era to be the correct balance of the game resembling its original launch state while also having ironed out some of the rough spots of launch. This version is also including some updates under the hood, like modern server infrastructure and Battle.net social features.

With the Classic beta now out it seems every related article somehow manages to spark the eternal war of "Vanilla was the best WoW sucks now" and "lol nostalgia goggles, Vanilla sucked, enjoy your two weeks of Classic". I have to say, even though I understand the principles behind the battle and the reasons people behave and talk this way... I actually REALLY don't get it on a deeper level.